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The galactose network has been extensively studied at the unicellular level to broaden our understanding of the regulatory mechanisms governing galactose metabolism in multicellular organisms. Although the key molecular players involved in the metabolic and regulatory processes of this system have been known for decades, their interactions and chemical kinetics remain incompletely understood. Mathematical models can provide an alternative method to study the dynamics of this network from a quantitative and a qualitative perspective. Here, we employ this approach to unravel the main properties of the galactose network, including equilibrium binary and temporal responses, as a way to decipher its adaptation to actively-changing inputs. We combine its two main components: the genetic branch, which allows for bistable responses, and a metabolic branch, encompassing the relevant metabolic processes that can be repressed by glucose. We use both computational tools to estimate model parameters based on published experimental data, as well as bifurcation analysis to decipher the properties of the system in various parameter regimes. Our model analysis reveals that the interplay between the inducer (galactose) and the repressor (glucose) creates a bistable regime which dictates the temporal responses of the system. Based on the same bifurcation techniques, we explain why the system is robust to genetic mutations and molecular instabilities. These findings may provide experimentalists with a theoretical framework with which they can determine how the galactose network functions under various conditions.

The expression level of tissue-restricted autoantigens (TSA) in the thymus is crucial for the negative selection of autoreactive T cells during central tolerance. The autoimmune regulator factor (AIRE) plays an important role in the positive regulation of these TSA in medullary thymic epithelial cells and, consequently, in the negative selection of high-avidity autoreactive T cells. Recent studies, however, revealed that thymic islet cell autoantigen (ICA69) expression level in non-obese diabetic (NOD) mice, prone to developing type 1 diabetes (T1D), is reduced due to an increase in the binding affinity of AIRE to the Ica1-promoter region, which regulates ICA69 protein synthesis. This seemed to suggest that AIRE acts as a transcriptional repressor of Ica1 gene in the thymus, causing down regulation in the expression level of ICA69. To investigate this hypothesis and the apparent dual role of AIRE in negative selection, we develop a series of mathematical models of increasing complexity describing the temporal dynamics of self-reactive T cells, AIRE-mRNA and AIRE-(in)dependent thymic TSA-associated genes. The goal is to understand how changing the binding affinity of AIRE to Ica1-promoter affects both T-cell tolerance and the dual role of the transcription factor. Using stability analysis and numerical computations, we show that the model possesses a bistable switch, consisting of healthy and autoimmune states, in the expression level of Ica1 gene with respect to AIRE binding affinity, and that it can capture the experimentally observed dual role of AIRE. We also show that the model must contain a positive feedback loop exerted by T cells on AIRE expression (e.g., via lymphotoxin released by T cells) to produce bistability. Our results suggest that the expression-level of AIRE-mRNA in the healthy state is lower than that of the autoimmune state, and that negative selection is very sensitive to parameter perturbations in T-cell avidity.

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